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What is the name of the red plactic screw in the picture? It's from a toilets flushing mechanism.
I would call it the float height adjustment screw, possibly tank water level height adjustment screw.
Older designed that had a more-or-less horizontal mechanism, that utilized a ball for a float, the connecting device was often called the float rod.
Here they call it a "link", but yours also performs the adjustment function.
Required, but never shown